Quintic B-spline method for time-fractional superdiffusion fourth-order differential equation

The main objective of this paper is to obtain the approximate solution of superdiffusion fourth-order partial differential equations. Quintic B-spline collocation method is employed for fractional differential equations (FPDEs). The developed scheme for finding the solution of the considered problem is based on finite difference method and collocation method. Caputo fractional derivative is used for time fractional derivative of order α, 1<α<2. The given problem is discretized in both time and space directions. Central difference formula is used for temporal discretization. Collocation method is used for spatial discretization. The developed scheme is proved to be stable and convergent with respect to time. Approximate solutions are examined to check the precision and effectiveness of the presented method.